Gordon Brown has announced a series of inquiries and safeguards to try to shore up public confidence following the loss of 25 million people’s personal details by HM Revenue and Customs.

The Prime Minister was forced to make a rare apology, when he told the House of Commons that he "profoundly regretted and apologised" for the loss of two computer discs with the information on.

But he came to the defence of his Chancellor, Alistair Darling, insisting there was no reason why any member of his cabinet should resign. The blunder by HM Customs and Revenue was at the top of the agenda as Mr Brown clashed with Conservative leader David Cameron in the Commons yesterday.

Every family claiming child benefit, including 672,220 in the West Midlands, has been warned to monitor their bank accounts for suspicious activity.

Some Labour MPs have expressed hopes that the Tories will lose points with the electorate for trying to make party political capital out of the affair. But the Prime Minister clearly realised that he needed to act, in order to convince voters this was a one-off mistake rather than part of a pattern of errors – not least because the Government hopes to press ahead with national computer database as part of its identity card scheme.

Mr Brown was able to set out his position at the start of Prime Minister's Questions yesterday, thanks to Labour backbencher Ann McKechin who helpfully asked whether he would "take every possible step to ensure the protection of data of our citizens."

The Prime Minister replied: "I profoundly regret and apologise for the inconvenience and worries that have been caused to millions of families who receive child benefit.

"When mistakes happen in enforcing procedures we have a duty to do everything we can to protect the public and that’s why bank accounts are being checked now for fraudulent activities."

He pointed out that review of Revenue and Customs handling of data by the chairman of PricewaterhouseCoopers had already been announced.

Mr Brown also revealed that he had ordered Cabinet Secretary Sir Gus O’Donnell and security experts to ensure every Government department and agency checked its own procedures for keeping data safe.

And he announced that Information Commissioner Richard Thomas is to be granted new powers to carry out spot checks on departments to ensure that they are doing everything they can to protect the privacy of details given them.

"We will do everything in our power to ensure data is safe," he said.

Mr Cameron, in a series of increasingly bad-tempered exchanges with Mr Brown, attempted to put forward two arguments.

He claimed firstly that the loss of data was part of a "systemic" failure to protect the public by government agencies. Second, he argued that the loss of the child benefit records demonstrated the folly of the ID card scheme, which the Tories oppose.

Challenged later on whether any ministers had offered their resignation, Mr Brown responded defiantly: "No, and nor should they."

And he gave an endorsement to Mr Darling, telling MPs "the Chancellor has done an excellent job, both as a former minister at the Treasury and now as Chancellor of the Exchequer".

However, there were indications yesterday that the loss of the records would give ammunition to opponents of identity cards on both sides of house, as some Labour MPs joined calls for Mr Brown to put the policy on hold.

Karen Buck, a member of the Commons Home Affairs Committee, called for a "pause" on further progress, in an interview following Prime Minister's Questions.

She said: "The worst thing in the world would be to plough on and say 'We’re going ahead with this' until we have had a chance for proper reflection and measure where public opinion stands when this has calmed down."

She was backed by Andy Love, a member of the Treasury Committee, who said: "It is sensible in the circumstances to stand back for a while."